'Rate' in the rate law

Question

I am slightly confused about what the rate is that is given by the rate law. Is it the rate of reaction (I.e. the rate of loss of reactant or formation of product divided by its stoichiometric coefficient?)

I suppose it would not make a difference to the rate equation itself if we simply used the rate of loss of reactant or formation of product without the factor of the stoichiometric coefficient, however then our rate constant would be multiplied by this factor. In that case we would have to specify what rate we are referring to when we are giving the rate constant.

My confusion stems from the fact that I have never seen it written that the rate constant is specifically determined for a given reaction, but I suppose it does not matter because rate laws are given as

$\frac {d [A]}{dt}='law'$

As opposed to just

$r='law'$

So when we actually write scientific papers we automatically specify in the expression of the equation what rate we are referring to. And then if we wished to transfer this rate law to give the change in concentration of another reactant or product we would use the stoichiometric relations and it would indeed change the value of the rate constant for a given rate law...

I apologise if I have not expressed myself clearly. I am starting out learning about this topic so have just looked at rate laws in theory and have not come across them in papers or seen how they are given in practice. Would appreciate if someone could verify if my thinking is correct or not?

Answer 1

Rate of reaction is related via stoichiometry to the rate of consumption of a reactant(r reactant) and the rate of formation of a product( r product), the rate of reaction-unique rate-( r r) can be determine by following the concentration of either a reactant or product as a function of time. The change in concentration with time is directly proportional to the rate of reaction, where the proportionality constant in the reciprocal of the stoiochiometric coefficient of the species in the balanced chemical reaction. So rr= r reactant or r product divided by the stoichiometric coefficient. So The mentioned equation for the rate(rr ) may be confusing since the stoichiometric coefficient value may vary if we write the balanced equation in other way.Thus the values of rr and and specific rate constant – unique rate constant K(r) may vary wih respect of the version of balanced equation. But the individual values of r product or r reactant and the rate constant of product or the rate constant of reactant remain same irrespective of the version of balanced equation , this is actually what we are measuring experimentally as rate. However, in this way, the rate with respect to different species and the rate constant of different species(K (reactant), K(product) ) will have different values. There are in fact an infinite number of possible rate equations and an infinite number of corresponding rate constants. The value of the "rate constant" k depends on how you define the rate.